If net force on particle is zero , show that linear momentum remains constant
Answers
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The second law states that the net force on a particle is equal to the time rate of change of its linear momentum p in an inertial reference frame:
where, since the law is valid only for constant-mass systems, the mass can be taken outside thedifferentiation operator by the constant factor rule in differentiation. Thus,
where F is the net force applied, m is the mass of the body, and a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it.
Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see below).
Consistent with the first law, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude; such is the case with uniform circular motion. The relationship also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum.
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